Zynga and Facebook are still dating, but they're now free to see others.

That's the upshot of a document the San Francisco gaming company filed Thursday afternoon with the Securities and Exchange Commission, driving Zynga's already deflated stock further downward.

Investors clearly worried about the loosening ties between Zynga and its most important source of revenue. The stock closed at $2.62 a share, near its all-time low, but it was down an additional 12 percent in after-hours trading once the SEC filing hit.

"The relationship between Facebook and Zynga has seemingly worsened," analyst Arvind Bhatia told Bloomberg News. Bhatia, who covers both companies for Sterne Agee & Leach, has been bearish on Zynga since before its IPO last year -- citing, in part, its dependence on Facebook.

Zynga derives the vast majority of its user traffic and revenue from the social network; in turn, Zynga represents a significant chunk of Facebook's user activity and 12 percent of the Menlo Park company's revenue last year.

Zynga's embattled chief executive, Mark Pincus, was one of the first investors in Facebook, along with PayPal co-founder Peter Thiel. But the gaming company and Facebook both have taken steps in recent months to reduce their interdependence.

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Facebook opened an "App Center" making it easier for competing gaming developers to reach users on its site.

Zynga, like some other social game makers, has moved increasingly toward mobile games; it also unveiled its own gaming website, Zynga.com, earlier this year, although that site currently runs on Facebook's platform.

The new SEC filing lays the groundwork to change that. Zynga said it will no longer be required to build its Web properties on Facebook or provide the social network with exclusive games.

Zynga also won't be required to display Facebook ads on Zynga.com. And visitors to the site won't have to use Facebook Credits to buy virtual goods there.

Those goods, which Zynga devotees use to build out their online worlds, represent most of the gaming company's revenue. Some developers have chafed under the requirement to use the currency because Facebook keeps 30 percent of every dollar users spend to buy credits.

Given the fact that so many of Zynga's users still access the company's games via Facebook, the change isn't likely to impact either company's bottom line in the near term.

More than 300 million of Zynga's monthly active users play games like "CityVille" and "Words With Friends" on Facebook; that was 10 times the number who played the games on mobile platforms. Even fewer play on the fledgling Zynga.com, at least so far.

One possible hindrance to Zynga's efforts to grow that traffic is that the revised agreement prevents the company from cross-promoting games between Zynga.com and Facebook. Up to now, users playing on Facebook have been able to click on links to play games on Zynga's own site; officials at both companies said that was a special privilege not shared by other gaming companies.

The new deal also gives Facebook, for the first time, the ability to develop its own games, which it previously had pledged not to do.

A Facebook spokeswoman, however, told this newspaper that the company has "absolutely no plans to build our own games."

It's been a rough week for social media companies, with deals site Living Social announcing plans to lay off 400 workers and rival Groupon, which, like Zynga, went public last year, reportedly the scene of a boardroom split about whether its CEO should resign.

Contact Peter Delevett at 408-271-3638. Follow him at Twitter.com/mercwiretap.